HP had just offered grim guidance on profits for the next quarter, and explained that most of that was because of foreign exchange rates. They insisted when measuring performance using constant currency, they would end 2015 with flat overall revenues. That means HP would stop shrinking.

"ES, this will be the key," Whitman said. "We expect better revenue performance from ES in the second half."

She described the situation like water draining out of the tub.

"Think of it like the bathtub and the water is going to stop draining out of the bathtub as fast as it has, so the water we pour in ought to lead to a rising level in the tub," Whitman said.

Then she qualified that even if ES revenue isn't exactly rising, she expects the unit to have "a much slower rate of decline by the end of the year .... But we have to continue to execute."

Cathie Lesjak agreed precisely that "HP ES is key" to flat revenues next year when comparing constant currency.

Earlier in the day, HP had announced a huge, 10-year, multi-billion customer contract with Deutsche Bank where the bank hired HP to build it a more efficient data center that uses "hybrid cloud" technology. Lesjak told analysts on the call that HP has also already won another big deal that hasn't been announced yet.

"Key account runoff that we've been talking about really abates in the second half of the year," she said.

In other words, the customers that have decided not to renew huge outsourcing contracts with HP will be mostly cleared out.

The situation isn't entirely HP's fault. Giant decade-long outsourcing contracts have gone out of vogue these days. Companies today are using more cloud computing, buying apps as a service, and updating their data centers to be less expensive and more efficient, a trend called hybrid computing.

But HP is also facing a ton of competition for this highly lucrative hybrid computing work from old competitors like IBM and new ones like Red Hat.

The numbers certainly show that the bleeding at HP Enterprise Services has to end. The group's revenue decreased 11% last quarter from a year ago. It dropped 7% the quarter before, 6% the previous quarter, and down by another 7%, and another 7% ... you get the idea.

This unit has seen its fair share of HP's 55,000 layoffs that are still going on. Employees at the unit tell us managers come and go like a drive-through.